Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#33569 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C59 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C23×C59 ◁ C22×Q8×C59 ◁ G | |
1082 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,13)(4,10)(5,18)(6,21)(7,12)(8,14)(9,17)(11,23)(15,28)(16,31)(19,25)(20,27)(22,24)(26,32)(29,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3)(2,8)(4,14)(5,19)(6,22)(7,15)(9,24)(10,28)(11,26)(12,25)(13,18)(16,23)(17,32)(20,30)(21,29)(27,31);(1,4,7,5)(2,9,12,27)(3,14,15,19)(6,20,23,17)(8,24,25,31)(10,11,18,21)(13,29,28,26)(16,32,22,30);(3,15)(8,25)(13,28)(14,19)(16,22)(24,31)(26,29)(30,32)2006 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26557);